In this paper it is shown that, when there is lack of coercivity with respect
to some partial derivatives on the underlying field $u$, then the relaxation
of the functional%
\[
u\mapsto\int_{\Omega}f\left( u,Du\right) \,dx
\]
may fail to be local. This result is applied to a singular perturbation model
for a membrane energy depending on deformations and out-of-plane bending.